{"status": "success", "data": {"description_md": "In triangle $ ABC$, $ AC = 13, BC = 14,$ and $ AB=15$. Points $ M$ and $ D$ lie on $ AC$ with $ AM=MC$ and $ \\angle ABD = \\angle DBC$. Points $ N$ and $ E$ lie on $ AB$ with $ AN=NB$ and $ \\angle ACE = \\angle ECB$. Let $ P$ be the point, other than $ A$, of intersection of the circumcircles of $ \\triangle AMN$ and $ \\triangle ADE$. Ray $ AP$ meets $ BC$ at $ Q$. The ratio $ \\frac{BQ}{CQ}$ can be written in the form $ \\frac{m}{n}$, where $ m$ and $ n$ are relatively prime positive integers. Find $ m-n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>In triangle $ ABC$, $ AC = 13, BC = 14,$ and $ AB=15$. Points $ M$ and $ D$ lie on $ AC$ with $ AM=MC$ and $ \\angle ABD = \\angle DBC$. Points $ N$ and $ E$ lie on $ AB$ with $ AN=NB$ and $ \\angle ACE = \\angle ECB$. Let $ P$ be the point, other than $ A$, of intersection of the circumcircles of $ \\triangle AMN$ and $ \\triangle ADE$. Ray $ AP$ meets $ BC$ at $ Q$. The ratio $ \\frac{BQ}{CQ}$ can be written in the form $ \\frac{m}{n}$, where $ m$ and $ n$ are relatively prime positive integers. Find $ m-n$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2010 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/10_aime_II_p14"}}